Word Problems 1
Consecutive Integers
Name:
Let’s work on some classic algebra word problems! Remember: Algebra exists to help us solve problems
that you can’t solve in your head. You should always start a problem by trying to figure it out without
algebra. If you can’t solve it that way, then algebra will come to your rescue!
Try this problem in your head:
Three positive consecutive integers have a sum of 9. What are the three integers?
Now try this problem. This is a trickier problem!
Five consecutive even integers have a sum of 10. What are the integers?
Algebra helps us solve trickier problems like the one above. Let’s see how it works.
Find the pattern and fill in the blank:
Consecutive Integer
Consecutive Even Integer
Consecutive Odd Integer
2, 3, ______, 5
6, 8, _______, 12
11, 13, _______
-4, -3, -2, _______
-16, _______, -12, -10
-19, ______, -15
How can we write an expression How can we write an expression How can we write an expression
for four consecutive integers?
for four consecutive even
for three consecutive odd
Let x = 1st integer
integers?
integers?
Try these!
1) If x +3 represents an integer, then the next consecutive integer in terms of x is
(1) x
(2) x +2
(3) x +4
(4) x +5
2) If x - 4 represents an odd integer, then the next consecutive odd integer in terms of x is
(1) x - 6
(2) x - 4
(3) x - 3
(4) x – 2
3) If n - 6 is an even integer, what is the next larger consecutive even integer?
Follow the leader: Look at each example below. Then try a problem that is like it.
Leader: Find two consecutive integers whose sum You: Find two consecutive integers
is 95
whose sum is 33.
Define Variables:
Define Variables:
Let n = the first integer.
Let n + 1 = the second integer
Equation:
n  n  1  95
Equation:
2n  1  95
1 1
2n 94

2
2
n  47
n  1  48
Answer: The two consecutive integers are 47 and Answer:_____________________________
48.
Leader: Find three consecutive odd integers whose You: Find two consecutive odd integers whose
sum is 45
sum is 36.
Define Variables:
Let n
Define Variables:
= the first integer.
Let n + 2 = the second integer
Let n + 4 = the third integer
Equation:
Equation:
n  n  2  n  4  45
3n  6  45
Continue solving
Answer:_____________________________